关于三重积分的计算

本文考虑学生学习数学分析的一个难点-三重积分的计算。首先对体V进行了分类,然后对各种类型的体V举例说明了计算方法.通过实践检验,用这样的方法,学生学习的效果很好.     

一类Fejer积分的计算

利用Wallis公式,Euler公式,分部积分公式及递推公式法得到了两类积分的递推公式,并由此求出了I_n(m)的递推公式,最后给出了I_n(1)-I_n(8)的具体求法.     

守恒积分与奇性场的定解方程

本文利用守恒积分,对HRR奇性场的角分布函数作了进一步的探讨.证明了角分布函数满足两个函数方程.并由此导出几种新的定解方程.对于平面应变及平面应力的情况分别给出函数方程与定解方程的具体公式.最后针对若干典型情况,给出了不同定解方程的精确的数值计算结果,验证了在一般情况下不同定解方程的等价性.     

Comparison of Some Trigonometric Integrals

Mathematical Notes - We show that Preiss–Thomson’s AS-integral is inconsistent with Burkill’s SCPintegral, James’ P2-integral, and Denjoy’s totalization T2s over the...     

定积分计算探讨

综合利用傅里叶级数法,参数求和法,参数展开法,得到了一些定积分的值.     

重积分的一般计算方法

本文通过总结重积分计算的一般解题方法和步骤,帮助初学者理清重要的知识脉络,提高处理重积分问题的能力.     

对称性在积分学中的应用

如果能充分利用积分区域的对称性和被积函数的奇偶性,高等数学中许多积分的计算过程将得到简化.总结并借助实例说明对称性在高等数学定积分、重积分以及曲线与曲面积分计算中的应用.     

三重积分计算浅析

本文首先讨论了不同坐标系中一例三重积分的计算,然后研究了变量置换在三重积分计算中的应用,指出它是三重积分在柱(球)坐标系中计算的本质,最后讨论了例题若干变形的处理,这些都有助于丰富和完善相关的教学内容与细节.     

The Calculation of Indefinite Integrals of B-splines

The purpose of this paper is to give a useful formula for theindefinite integral of a B-spline. We show that the formuladoes not introduce any redundant knots, and, when used in conjunctionwith Cox's algorithm (1972), provides a very convenient methodfor computing the indefinite integral.     

Fractional Smoothness of Some Stochastic Integrals

We study the fractional smoothness in the sense of Malliavin calculus of stochastic integrals of the form ∫0^1Ф（Xs）dXs, where Xs is a semimartingale and Ф belongs to some fractional Sobolev space over R.     

SOME TWO-INDEPENDENT-VARIABLE INEQUALITIES INVOLVING IMPROPER INTEGRALS

In the paper the authors establish four theorems on two-independent-variableGronwall-type inequalities involving improper integrals with infinite integration limits.The results obtained improve and generalize the main results proved in the recent paper[5] by A.Corduneanu.Two classes of nonlinear continuous functions defined by F.M.Dannan[6] are applied in this article.And the results can be used as handy tools in thestudy of many Volterra integral and integro-differential equations with improper integralfunctionals.     

第一类曲面积分的一类特殊解法

对一些特殊曲面(如柱面、旋转曲面)上的第一类曲面积分,转化为二重积分的基本方法可能非常复杂,用类似计算三重积分的平行截面法能更简洁地解决此类问题.     

第二类曲面积分的计算方法

针对第二类曲面积分的计算进行探讨,指出计算时可以把曲面方程代入到被积函数中,且可以利用轮换对称性及奇偶性来简化计算,并提出可以利用公式法、高斯公式、两类曲面积分之间的关系及合一投影法四种方法来计算第二类曲面积分.     

Some Integrals Involving -Functions and Laguerre Polynomials

Ukrainian Mathematical Journal - Our aim is to establish some new integral formulas involving -functions associated with Laguerretype polynomials. We also show that the main results presented in...     

关于K-拟可加模糊积分的几点注记

在K-拟可加模糊积分定义及积分转换定理的基础上，证明这种模糊积分恰好构成K-拟可加模糊测度，并依据积分转换定理讨论这种K-拟可加模糊积分的一些补充性质。     

p—级数与几个广义积分

本文给出了ｐ—级数与广义积分∫１０ｌｎｋ－１ｘ１－ｘｄｘ，∫１０ｌｎｋ－１ｘ１＋ｘｄｘ，∫１０ｌｎｋ－１ｘ１－ｘ２ｄｘ，∫１０ｌｎｋ－１ｘ１＋ｘ２ｄｘ之间的关系．并通过一些ｐ—级数的求和，给出了上述广义积分中某些积分的积分值．     

Some Remarkable Properties of Sinc and Related Integrals

Using Fourier transform techniques, we establish inequalities for integrals of the form We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications.     

Calculation of Improper Integrals Using (nα)-Sequences

 We give a necessary and sufficient condition for the relation to hold as . Here α is an irrational number, denotes the fractional part of x and f is from a suitable class of functions with the property that or for a finite set of rational . Received 11 January 2001; in revised form 10 August 2001     

A Boundedness Result for Minimizers of Some Polyconvex Integrals

We consider polyconvex functionals of the Calculus of Variations defined on maps from the three-dimensional Euclidean space into itself. Counterexamples show that minimizers need not to be bounded. We find conditions on the structure of the functional, which force minimizers to be locally bounded.